Unit Groups Of Classical Rings

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Unit Groups Of Classical Rings

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Author : Gregory Karpilovsky
language : en
Publisher:
Release Date : 1988

Unit Groups Of Classical Rings written by Gregory Karpilovsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

The purpose of this book is to give a self-contained, up-to-date account of the structure of unit groups of classical rings. In so doing, the work draws together four areas of mathematics: ring theory, group theory, group representation theory, and algebraic number theory. The ensuing interplay between these disciplines provides a unique source of enrichment for each of them. The main theme centers on two related problems: to determine the isomorphism class of the unit group (U)R of ring R in terms of natural invariants associated with R; and to find an effective method for the construction of units of ring R. Various threads of the development are tied together to convey a comprehensive picture of the current state of the subject. Examples are provided to help research workers who need to compute explicitly unit groups of certain rings. A familiarity with basic ring-theoretic and group-theoretic concepts is assumed, but a chapter on algebraic preliminaries is included. The text is distinguished by its very clear exposition.

Unit Groups Of Group Rings

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Author : Gregory Karpilovsky
language : en
Publisher:
Release Date : 1989

Unit Groups Of Group Rings written by Gregory Karpilovsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Commutative rings categories.

It is the purpose of this book to provide a detailed account of the structure of the group U(RG) and to provide a systematic account of recent research and results.

Exercises In Classical Ring Theory

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Author : T.Y. Lam
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Exercises In Classical Ring Theory written by T.Y. Lam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

Based in large part on the comprehensive "First Course in Ring Theory" by the same author, this book provides a comprehensive set of problems and solutions in ring theory that will serve not only as a teaching aid to instructors using that book, but also for students, who will see how ring theory theorems are applied to solving ring-theoretic problems and how good proofs are written. The author demonstrates that problem-solving is a lively process: in "Comments" following many solutions he discusses what happens if a hypothesis is removed, whether the exercise can be further generalized, what would be a concrete example for the exercise, and so forth. The book is thus much more than a solution manual.

Structure Theorems Of Unit Groups

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Author : Eric Jespers
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-11-13

Structure Theorems Of Unit Groups written by Eric Jespers and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-13 with Mathematics categories.

This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.

Methods In Ring Theory

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Author : Vesselin Drensky
language : en
Publisher: CRC Press
Release Date : 2021-02-28

Methods In Ring Theory written by Vesselin Drensky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-28 with Mathematics categories.

"Furnishes important research papers and results on group algebras and PI-algebras presented recently at the Conference on Methods in Ring Theory held in Levico Terme, Italy-familiarizing researchers with the latest topics, techniques, and methodologies encompassing contemporary algebra."

Orders And Generic Constructions Of Units

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Author : Eric Jespers
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-11-13

Orders And Generic Constructions Of Units written by Eric Jespers and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-13 with Mathematics categories.

This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.

Groups 93 Galway St Andrews Volume 2

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Author : C. M. Campbell
language : en
Publisher: Cambridge University Press
Release Date : 1995-03-16

Groups 93 Galway St Andrews Volume 2 written by C. M. Campbell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-16 with Mathematics categories.

This two-volume book contains selected papers from the international conference 'Groups 1993 Galway / St Andrews' which was held at University College Galway in August 1993. The wealth and diversity of group theory is represented in these two volumes. As with the Proceedings of the earlier 'Groups-St Andrews' conferences it is hoped that the articles in these Proceedings will, with their many references, prove valuable both to experienced researchers and also to new postgraduates interested in group theory.

Rings Modules Algebras And Abelian Groups

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Author : Alberto Facchini
language : en
Publisher: CRC Press
Release Date : 2020-02-10

Rings Modules Algebras And Abelian Groups written by Alberto Facchini and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-10 with Mathematics categories.

Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological

Groups Rings And Group Rings

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Author : A. Giambruno
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Groups Rings And Group Rings written by A. Giambruno and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

Represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28 - August 2, 2008, in Ubatuba, Brazil. This title contains results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras.

Unit Groups Of Group Rings

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Author : Gregory Karpilovsky
language : en
Publisher: Longman Scientific and Technical
Release Date : 1989

Unit Groups Of Group Rings written by Gregory Karpilovsky and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.